Measures Of Central Tendency

Question 1

What is the formula for arithmetic mean for ungrouped data?

Answer 1

X = Σfx/n

Question 2

What is the formula for the mean of ungrouped data with large frequency?

Answer 2

x̄ = Σfx / Σf

Question 3

What is the formula for weighted arithmetic mean?

Answer 3

x̄ = ΣWx / ΣW

Where W = the weight

Question 4

What is the formula for mean for grouped data (with no assumed mean)?

Answer 4

x̄ = Σfx / Σf

Question 5

What is the formula for mean for grouped data when given assumed mean?

Answer 5

x̄ = A + (Σfd/Σf)

A = assumed mean

d = x - A; where X is class mark

Question 6

What is the formula for median for ungrouped data when n is odd?

Answer 6

(n+1/2)th value

Question 7

What is the formula for median for ungrouped data when n is even?

Answer 7

The arithmetic mean of (n/2)th value and (n+2/2)th value.

Question 8

What is the formula for grouped median?

Answer 8

Lcb + i [ (Σf/2 - Cfb) ÷ f-median ]

Where Lcb = lower class boundary
I = class width

Cfb = cumulative frequency before the median frequency

f-median = frequency of the median class

Question 9

What is the formula for mode for grouped data?

Answer 9

Lcb + i [(fm - FB) / 2fm - fb - fa]

fm = modal frequency
Fb = frequency before modal frequency
fa = frequency after

Question 10

What is the empirical relationship for unimodal frequency curves that are moderately skewed?

Answer 10

mean - mode = 3(mean - median)

Question 11

What is geometric mean?

Answer 11

For a series containing ‘n’ observations, it is the nth root of product of values.

Question 12

What is the formula for geometric mean in ungrouped data for a set of N positive numbers like X1, X2, X3 … xn? (Expressed in logarithms)

Answer 12

GM = antilog(Σlogx/N)

Question 13

What is the geometric mean for a set of ungrouped N positive numbers, x1, x2, …, xn? (Without log)

Answer 13

(x1 • x2 • x3 • … • xn)^(1/n)

Therefore, the nth root of the product of the series of numbers.

Question 14

What is the geometric mean for a set of ungrouped N positive numbers, x1, x2, …, xn (Without log) with corresponding frequencies f1, f2, f3, … fn?

Answer 14

(x1^f1 • x2^f2 • x3^f3 • … • xn^fn)^[1/Σf]

Question 15

What is the geometric mean for grouped data?

Answer 15

(x1^f1 • x2^f2 • x3^f3 • … • xn^fn)^[1/Σf]

Question 16

What is the geometric mean for grouped data (with log)?

Answer 16

GM = antilog [(Σf•logx)/Σf]

Question 17

What is harmonic mean?

Answer 17

This is the reciprocal of the arithmetic mean of the reciprocal of the values of each observation.

Question 18

What is the formula for harmonic mean for ungrouped data?

Answer 18

HM = N/[Σ(x^-1)]

Question 19

What is the harmonic mean for ungrouped data with corresponding frequencies?

Answer 19

HM = Σf/[Σf(x^-1)]

Question 20

What is the formula for harmonic mean for grouped data?

Answer 20

HM = Σf/[Σf(x^-1)]

Question 21

What is the relationship between arithmetic mean, geometric mean, and harmonic mean?

Answer 21

AM × HM = GM²

Question 22

What is the formula for grouped population standard deviation?

Answer 22

Here

Question 23

Formula for sample standard deviation in ungrouped.

Answer 23

Here.